The invention relates to calculating the multiplicative inversion of a Galois field element in GF(q.sup.m), when this element is provided in vectorial representation. Herein, q is a prime raised to an exponent, usually, but not exclusively being q=2.sup.1 =2. For many applications, m is even and often equal to m=8. Such calculations then represent byte-wise data processing for purposes of cryptography, error protection such as by means of Reed-Solomon codes, fast Fourier transform, and others. The data then corresponds to video data, audio data wherein a -Compact Disc- or -Digital Audio Tape- recording audio sample would be constituted by two bytes, or measuring results. As reference the U.S. Pat. No. 4,587,627 is called upon. Hereinafter elementary properties and calculatory operations in a Galois field are considered standard knowledge. Generally, any Galois field element may be inverted by means of a translation table (PROM or ROM), which for reasonable fields, such as GF(2.sup.8) requires a very extensive amount of hardware, inasmuch for each of 2.sup.8 different possible input combinations an 8-bit output were required. An alternative method using, for example, a programmed processor would require heavy pipelining and in consequence, much computational delay. The present invention uses the concept of subfields and in particular, calculates the multiplicative inverse of a vectorially represented element of a finite field, the major field, by means of inversion in a subfield of the major field. Now, a finite field GF(q.sup.m) contains GF(q.sup.n) as a subfield if m=rn, wherein for disclosing the present invention, an example is described wherein r=2. However, the principle of the invention is just as well applicable to other values of r. The index of the major field over the subfield is r. Now, inasmuch as a calculation in a subfield operates on fewer vector coefficients than a corresponding operation in the major field, the former calculation is easier and/or faster.